Optimized aerodynamic profile for a turbine vane, in particular for a nozzle of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P 0  situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P 1 . The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority to U.S. Patent Application No. 62/504,554, filed on May 11, 2017, the entirety of which is incorporated by reference herein.

INTRODUCTION

The present disclosure relates to an aerodynamic profile for a turbine vane.

In particular, the disclosure relates to the aerodynamic profile of a nozzle vane forming a portion of the stator of a gas turbine, and more particularly of a low pressure turbine of the type used in a turbojet of an aircraft.

The disclosure relates in particular to a nozzle vane of a turbine having a plurality of stages, preferably five stages.

Such a profile should enable the turbine to provide the desired efficiency, and in order to do that it must be such that the flow of air around the profile is sound over the working spectrum of the turbine, i.e. substantially such that it does not give rise to turbulence, which is harmful for overall efficiency.

It must be capable of being installed properly in the environment of the engine, and in particular, for a nozzle vane forming a portion of the stator of the turbine, it must be capable of being fastened easily to the sectors of the foot platform (the zone of the vane that is furthest from the axis of rotation of the turbine) and of the head platform (the zone that is closest to said axis). Furthermore, this part must present a profile enabling it to be manufactured in a reliable and cost-effective manner by available manufacturing methods, such as casting, forging, machining, additive fabrication, or else weaving, without this list being limitative.

Furthermore, the profile of the vane must enable it to withstand the mechanical stresses, to which the vane is subjected, by enabling those stresses to be spread over the entire vane in such a manner as to avoid premature wear thereof. This spreading must apply both in static mode and in dynamic mode.

An object of the disclosure is to propose an aerodynamic profile for a turbine vane that is optimized, and capable of satisfying those objectives.

This object is achieved by the fact that when cold and in a non-coated state, said profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point P under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane that is the intersection of the stacking axis of the vane and the axisymmetric surface of the hub, out to a second reference plane that is the intersection of said stacking axis with the axisymmetric surface of the casing, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.

This profile has been determined as a result of numerous tests and simulations. It is defined cold, i.e. at an ambient temperature of 20° C. That is a reference temperature at which the profile is geometrically determined. The above-mentioned objectives of aerodynamics and mechanical optimization are naturally valid for the conditions of use of this aerodynamic profile, i.e. when hot, at a temperature that is stabilized when the engine of which the turbine forms a part is being used under cruising conditions.

Furthermore, the aerodynamic profile of the disclosure is defined in the non-coated state. Since turbine vanes are subjected to high temperature gradients, it is common practice for them to be provided with a coating having thermal properties enabling them more easily to withstand such temperature variations. The profile is determined prior to installing such a coating.

It is stated above that the profile of the disclosure is “substantially identical” to the nominal profile. This means that the profile may depart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of ±1 millimeter (mm) in a direction normal to the surface of the nominal profile.

It is also preferable for the X,Y coordinates of the aerodynamic profile to lie within a range of ±5% relative to the X,Y coordinates of the nominal profile.

In addition, the aerodynamic profile may be positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the radial axis of the vane, along which the coordinate Zadim is measured.

These variations take account in particular to at least one of manufacturing tolerances of the profile, the setting of the profile to adapt to the environment when in operation, and possible deformation occurring when mounting the vane and integrating the same in the nozzle.

With a nozzle vane, i.e. a portion of the stator of a turbine, the profile serves to orient the fluid correctly for the turbine blades that are situated downstream, and that belong in particular to the rotary wheel of the same stage of the turbine.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be better understood and its advantages appear better on reading the following detailed description of an embodiment given by way of non-limiting example. The description refers to the accompanying drawings, in which:

FIG. 1 is a fragmentary axial diagrammatic section view of a turbine including a vane of profile that corresponds to that of the present disclosure;

FIG. 2 shows a vane of the turbine.

DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises five stages referenced respectively S1 to S5. In the direction DF going from upstream to downstream, each stage comprises a nozzle that forms a portion of the stator of the turbine and that has a plurality of radially-oriented vanes, and a rotary wheel that forms a portion of the rotor of the turbine and that likewise includes a plurality of radially-oriented blades.

In FIG. 1, the vanes of the nozzles of stages S1 to S5 are given references N1 to N5 (these vanes are shown in dashed lines, for ease of representation), whereas the blades of rotary wheels of stages S1 to S5 are given respective references W1 to W5.

In known manner, the vanes of the nozzles are fastened at both ends to stationary structure portions, while the blades of the rotary wheels are fastened to a rotary disk via their roots that are formed at their radially-inner ends closer to the axis of the rotation A of the turbine. The disks forming parts of the wheels W1 to W5 are constrained to rotate together.

The disclosure relates a vane of one of the nozzles of the turbine that, as mentioned above, preferably comprises five stages as shown, without this number being limiting.

As best seen in FIG. 2, via its foot 10, which is its end remote from the axis of rotation A, the vane is fastened to the outer ring of the turbine, which ring is stationary in rotation. Via its head 14, formed by its end closer to the axis of rotation A, the vane is fastened to an inner shroud of the turbine. By convention, the aerodynamic profile 18 of the vane is the entire portion of said vane that extends radially outwards from its head 14 to its foot 10 without incorporating the fastenings respectively to the outer ring and to the inner shroud.

In FIG. 2, there can be seen a frame of reference comprising Cartesian coordinates X,Y,Z. The radial direction Z is the height direction of the vane, which extends radially from its head to its foot. This direction Z is perpendicular to the axial direction X which is the direction of the axis of rotation A of the turbine. The direction Y is perpendicular to the X,Z plane and is therefore tangential to the direction of rotation of the turbine.

The nominal profile from which the aerodynamic profile of the disclosure is determined is defined in following Table 1 of coordinates, in which the coordinate Zadim, measured along the axis Z is non-dimensional, whereas the dimensions X and Y, respectively measured along the axes X and Y, are expressed in millimeters.

TABLE 1 X Y Zadim −19.833 2.15536 −0.29044 −19.8398 2.100295 −0.29044 −19.8413 2.019771 −0.29044 −19.8237 1.896919 −0.29044 −19.7566 1.737232 −0.29044 −19.6112 1.56354 −0.29044 −19.3829 1.396779 −0.29044 −19.0752 1.249975 −0.29044 −18.6972 1.1146 −0.29044 −18.2481 1.001498 −0.29044 −17.73 0.919987 −0.29044 −17.1474 0.875888 −0.29044 −16.5053 0.871346 −0.29044 −15.8085 0.905947 −0.29044 −15.0617 0.978391 −0.29044 −14.2694 1.087861 −0.29044 −13.4364 1.234762 −0.29044 −12.5679 1.420794 −0.29044 −11.6697 1.648348 −0.29044 −10.7488 1.91974 −0.29044 −9.81302 2.236553 −0.29044 −8.87053 2.599401 −0.29044 −7.92901 3.007927 −0.29044 −6.99534 3.460822 −0.29044 −6.07541 3.955904 −0.29044 −5.17563 4.489329 −0.29044 −4.30248 5.055655 −0.29044 −3.4613 5.648766 −0.29044 −2.65638 6.26215 −0.29044 −1.8911 6.889151 −0.29044 −1.1681 7.523183 −0.29044 −0.48945 8.157746 −0.29044 0.14331 8.786312 −0.29044 0.733225 9.398417 −0.29044 1.282586 9.985737 −0.29044 1.793611 10.54107 −0.29044 2.268125 11.05841 −0.29044 2.708205 11.5323 −0.29044 3.112244 11.9614 −0.29044 3.479168 12.34468 −0.29044 3.808743 12.68122 −0.29044 4.100787 12.97101 −0.29044 4.353809 13.21642 −0.29044 4.565508 13.42194 −0.29044 4.695748 13.62407 −0.29044 4.724954 13.8112 −0.29044 4.699102 13.94951 −0.29044 4.664101 14.04178 −0.29044 4.633724 14.09574 −0.29044 4.605565 14.13427 −0.29044 4.575794 14.16824 −0.29044 4.532164 14.20708 −0.29044 4.453583 14.25654 −0.29044 4.326898 14.30171 −0.29044 4.150198 14.28867 −0.29044 3.955494 14.17073 −0.29044 3.769458 13.96319 −0.29044 3.54857 13.71394 −0.29044 3.285992 13.42731 −0.29044 2.98053 13.10365 −0.29044 2.630145 12.7451 −0.29044 2.233533 12.35422 −0.29044 1.79 11.93392 −0.29044 1.299571 11.48732 −0.29044 0.763117 11.01756 −0.29044 0.181903 10.52815 −0.29044 −0.44299 10.02352 −0.29044 −1.10913 9.507297 −0.29044 −1.81293 8.982172 −0.29044 −2.55044 8.450822 −0.29044 −3.31696 7.915238 −0.29044 −4.10725 7.376939 −0.29044 −4.9179 6.840382 −0.29044 −5.74761 6.313757 −0.29044 −6.59602 5.807902 −0.29044 −7.46132 5.332318 −0.29044 −8.33989 4.893357 −0.29044 −9.22483 4.492092 −0.29044 −10.1091 4.128366 −0.29044 −10.9855 3.802954 −0.29044 −11.8473 3.516529 −0.29044 −12.6881 3.269837 −0.29044 −13.5019 3.063496 −0.29044 −14.2833 2.897576 −0.29044 −15.0279 2.774023 −0.29044 −15.7306 2.692533 −0.29044 −16.3859 2.650004 −0.29044 −16.9889 2.640397 −0.29044 −17.5366 2.654175 −0.29044 −18.028 2.678112 −0.29044 −18.4644 2.696495 −0.29044 −18.8468 2.693902 −0.29044 −19.1727 2.659318 −0.29044 −19.4349 2.591033 −0.29044 −19.6289 2.497242 −0.29044 −19.7468 2.383613 −0.29044 −19.8005 2.279468 −0.29044 −19.0895 1.429476 −0.15825 −19.0999 1.374135 −0.15825 −19.1051 1.292497 −0.15825 −19.0895 1.167619 −0.15825 −19.0209 1.005588 −0.15825 −18.8746 0.828127 −0.15825 −18.6473 0.652969 −0.15825 −18.3419 0.489867 −0.15825 −17.9619 0.344405 −0.15825 −17.5101 0.220759 −0.15825 −16.9891 0.124811 −0.15825 −16.4019 0.063162 −0.15825 −15.7531 0.042041 −0.15825 −15.0474 0.066256 −0.15825 −14.2905 0.13917 −0.15825 −13.4887 0.26319 −0.15825 −12.6489 0.441617 −0.15825 −11.7785 0.67664 −0.15825 −10.8848 0.968165 −0.15825 −9.97426 1.31365 −0.15825 −9.05429 1.711887 −0.15825 −8.13379 2.164161 −0.15825 −7.22306 2.672639 −0.15825 −6.33092 3.235325 −0.15825 −5.46228 3.844446 −0.15825 −4.6209 4.491356 −0.15825 −3.80297 5.158851 −0.15825 −3.01265 5.841497 −0.15825 −2.25418 6.534212 −0.15825 −1.5315 7.23191 −0.15825 −0.8482 7.92948 −0.15825 −0.20623 8.62064 −0.15825 0.396142 9.296485 −0.15825 0.960531 9.949158 −0.15825 1.485337 10.57435 −0.15825 1.971892 11.16595 −0.15825 2.423243 11.7173 −0.15825 2.841076 12.22359 −0.15825 3.224782 12.68254 −0.15825 3.570611 13.09539 −0.15825 3.879156 13.4606 −0.15825 4.151489 13.77716 −0.15825 4.386931 14.04655 −0.15825 4.583253 14.27275 −0.15825 4.700281 14.48712 −0.15825 4.720243 14.67682 −0.15825 4.685719 14.81665 −0.15825 4.644519 14.90752 −0.15825 4.610186 14.9602 −0.15825 4.579056 14.99732 −0.15825 4.54696 15.02967 −0.15825 4.500432 15.06607 −0.15825 4.417784 15.11074 −0.15825 4.28765 15.14703 −0.15825 4.109945 15.1182 −0.15825 3.92342 14.98528 −0.15825 3.741871 14.7702 −0.15825 3.525638 14.51259 −0.15825 3.270649 14.21411 −0.15825 2.975867 13.87483 −0.15825 2.64007 13.49593 −0.15825 2.262615 13.07905 −0.15825 1.843281 12.62633 −0.15825 1.382258 12.14037 −0.15825 0.880106 11.62424 −0.15825 0.338847 11.08031 −0.15825 −0.24058 10.51266 −0.15825 −0.85758 9.926433 −0.15825 −1.50849 9.324164 −0.15825 −2.19113 8.710421 −0.15825 −2.90201 8.088801 −0.15825 −3.63884 7.464645 −0.15825 −4.39984 6.844407 −0.15825 −5.18386 6.23589 −0.15825 −5.98964 5.647587 −0.15825 −6.81508 5.087628 −0.15825 −7.65629 4.562329 −0.15825 −8.50723 4.074831 −0.15825 −9.36069 3.626159 −0.15825 −10.2094 3.216537 −0.15825 −11.0476 2.848443 −0.15825 −11.8709 2.527241 −0.15825 −12.6745 2.257915 −0.15825 −13.4525 2.042999 −0.15825 −14.198 1.881927 −0.15825 −14.9043 1.771904 −0.15825 −15.5651 1.70867 −0.15825 −16.175 1.686388 −0.15825 −16.7297 1.697246 −0.15825 −17.2268 1.729501 −0.15825 −17.6653 1.770364 −0.15825 −18.0463 1.806387 −0.15825 −18.3713 1.822239 −0.15825 −18.6403 1.808125 −0.15825 −18.848 1.748651 −0.15825 −18.981 1.650247 −0.15825 −19.0465 1.551642 −0.15825 −18.6429 −0.07823 0 −18.6539 −0.13555 0 −18.6578 −0.22032 0 −18.6348 −0.3486 0 −18.55 −0.51032 0 −18.3846 −0.6821 0 −18.1391 −0.85008 0 −17.8166 −1.00774 0 −17.4199 −1.15139 0 −16.9506 −1.27654 0 −16.4105 −1.37662 0 −15.802 −1.44295 0 −15.1294 −1.4661 0 −14.398 −1.43689 0 −13.6146 −1.34787 0 −12.7883 −1.19123 0 −11.9282 −0.96246 0 −11.044 −0.65953 0 −10.1455 −0.28195 0 −9.24293 0.170372 0 −8.34594 0.695024 0 −7.46268 1.286806 0 −6.60029 1.939343 0 −5.76471 2.645144 0 −4.96071 3.39601 0 −4.19153 4.182825 0 −3.45623 4.993555 0 −2.75554 5.818904 0 −2.08722 6.647985 0 −1.44849 7.470495 0 −0.83985 8.279429 0 −0.26272 9.068937 0 0.282221 9.833106 0 0.794294 10.56657 0 1.272435 11.26477 0 1.716441 11.92316 0 2.125514 12.53826 0 2.500604 13.10607 0 2.840804 13.62461 0 3.146544 14.09178 0 3.417793 14.50663 0 3.655086 14.86872 0 3.858922 15.1786 0 4.028319 15.43872 0 4.125058 15.6732 0 4.128397 15.86881 0 4.078029 16.01133 0 4.025441 16.0997 0 3.983864 16.14994 0 3.94732 16.18439 0 3.910599 16.21382 0 3.858248 16.24563 0 3.767711 16.28103 0 3.630087 16.29977 0 3.451622 16.24049 0 3.281249 16.07783 0 3.10994 15.84245 0 2.905959 15.56071 0 2.66802 15.23175 0 2.395686 14.85507 0 2.088791 14.43085 0 1.747568 13.95987 0 1.372532 13.4435 0 0.964127 12.88395 0 0.522058 12.28463 0 0.047967 11.64822 0 −0.45781 10.97896 0 −0.99496 10.28169 0 −1.56335 9.561934 0 −2.16258 8.825594 0 −2.79297 8.079679 0 −3.45321 7.330397 0 −4.14135 6.583845 0 −4.85481 5.845946 0 −5.59174 5.123698 0 −6.3514 4.425709 0 −7.13201 3.760241 0 −7.9296 3.133777 0 −8.73943 2.552153 0 −9.55851 2.024123 0 −10.3819 1.556779 0 −11.2022 1.153695 0 −12.0117 0.817446 0 −12.8024 0.550378 0 −13.5661 0.353409 0 −14.2937 0.222859 0 −14.9766 0.150769 0 −15.6073 0.128 0 −16.181 0.142978 0 −16.6946 0.18142 0 −17.1477 0.228008 0 −17.5414 0.267812 0 −17.8774 0.28909 0 −18.1561 0.282989 0 −18.374 0.23342 0 −18.5198 0.143585 0 −18.5945 0.046525 0 −18.6071 −0.37778 0.056652 −18.6184 −0.43602 0.056652 −18.6219 −0.52219 0.056652 −18.5966 −0.65218 0.056652 −18.5066 −0.8146 0.056652 −18.335 −0.98576 0.056652 −18.0832 −1.15297 0.056652 −17.7541 −1.31039 0.056652 −17.3502 −1.45455 0.056652 −16.873 −1.58094 0.056652 −16.3241 −1.68277 0.056652 −15.7059 −1.7513 0.056652 −15.0223 −1.77717 0.056652 −14.2789 −1.75069 0.056652 −13.4824 −1.6616 0.056652 −12.6428 −1.50177 0.056652 −11.7694 −1.26632 0.056652 −10.8731 −0.95172 0.056652 −9.96467 −0.55703 0.056652 −9.05427 −0.08386 0.056652 −8.15237 0.465642 0.056652 −7.26849 1.087212 0.056652 −6.40936 1.772701 0.056652 −5.57988 2.512746 0.056652 −4.78396 3.297962 0.056652 −4.02458 4.118894 0.056652 −3.29958 4.962556 0.056652 −2.60992 5.819976 0.056652 −1.95122 6.67871 0.056652 −1.32171 7.529569 0.056652 −0.72765 8.369602 0.056652 −0.16994 9.192305 0.056652 0.353878 9.989504 0.056652 0.845854 10.75402 0.056652 1.3069 11.48005 0.056652 1.736657 12.16321 0.056652 2.134912 12.79963 0.056652 2.50069 13.38663 0.056652 2.833585 13.92185 0.056652 3.133021 14.40386 0.056652 3.398635 14.83189 0.056652 3.630817 15.20563 0.056652 3.830021 15.52567 0.056652 3.995692 15.79409 0.056652 4.091017 16.03373 0.056652 4.09227 16.23202 0.056652 4.03881 16.37659 0.056652 3.983567 16.46512 0.056652 3.940081 16.51515 0.056652 3.901967 16.5491 0.056652 3.863788 16.57783 0.056652 3.809416 16.6083 0.056652 3.716073 16.64051 0.056652 3.575923 16.65249 0.056652 3.397453 16.5814 0.056652 3.233882 16.40741 0.056652 3.066243 16.16374 0.056652 2.866884 15.87196 0.056652 2.634895 15.53092 0.056652 2.369889 15.14004 0.056652 2.071656 14.69955 0.056652 1.740305 14.21032 0.056652 1.375861 13.67407 0.056652 0.978245 13.09334 0.056652 0.546755 12.47184 0.056652 0.082059 11.81297 0.056652 −0.41454 11.12033 0.056652 −0.94138 10.39777 0.056652 −1.49738 9.650077 0.056652 −2.08274 8.883511 0.056652 −2.69593 8.103471 0.056652 −3.33753 7.317497 0.056652 −4.00805 6.533648 0.056652 −4.70761 5.760346 0.056652 −5.43516 5.005563 0.056652 −6.18835 4.276704 0.056652 −6.96175 3.578278 0.056652 −7.75412 2.919681 0.056652 −8.5638 2.310977 0.056652 −9.38643 1.760055 0.056652 −10.2156 1.272612 0.056652 −11.0443 0.853526 0.056652 −11.8642 0.506225 0.056652 −12.6669 0.23285 0.056652 −13.4428 0.032775 0.056652 −14.1823 −0.09859 0.056652 −14.8765 −0.16853 0.056652 −15.5174 −0.1879 0.056652 −16.1002 −0.17036 0.056652 −16.622 −0.12943 0.056652 −17.0821 −0.08034 0.056652 −17.482 −0.03846 0.056652 −17.8231 −0.0145 0.056652 −18.1063 −0.01977 0.056652 −18.3284 −0.06682 0.056652 −18.4788 −0.15453 0.056652 −18.5567 −0.25155 0.056652 −18.6341 0.298782 0.093853 −18.6482 0.240482 0.093853 −18.6553 0.153597 0.093853 −18.6342 0.021395 0.093853 −18.548 −0.14542 0.093853 −18.3799 −0.32366 0.093853 −18.1313 −0.50133 0.093853 −17.8049 −0.67306 0.093853 −17.4029 −0.83556 0.093853 −16.9265 −0.98434 0.093853 −16.3769 −1.11241 0.093853 −15.7557 −1.21056 0.093853 −15.0666 −1.26881 0.093853 −14.3146 −1.27695 0.093853 −13.5061 −1.22479 0.093853 −12.6506 −1.10291 0.093853 −11.7579 −0.90463 0.093853 −10.8392 −0.62506 0.093853 −9.90558 −0.26296 0.093853 −8.96733 0.179289 0.093853 −8.03499 0.699586 0.093853 −7.11872 1.294356 0.093853 −6.22615 1.956133 0.093853 −5.36294 2.675724 0.093853 −4.53345 3.443509 0.093853 −3.74023 4.249074 0.093853 −2.98516 5.08245 0.093853 −2.26771 5.932567 0.093853 −1.58705 6.789237 0.093853 −0.94037 7.641708 0.093853 −0.32558 8.480708 0.093853 0.257157 9.299298 0.093853 0.807789 10.091 0.093853 1.326886 10.84947 0.093853 1.815068 11.56897 0.093853 2.271558 12.24526 0.093853 2.696191 12.87435 0.093853 3.088063 13.45343 0.093853 3.446346 13.98038 0.093853 3.770258 14.45385 0.093853 4.058837 14.87347 0.093853 4.311722 15.2394 0.093853 4.528756 15.55267 0.093853 4.709409 15.81538 0.093853 4.818907 16.05203 0.093853 4.830242 16.25204 0.093853 4.783011 16.40066 0.093853 4.730834 16.49231 0.093853 4.688577 16.54433 0.093853 4.650915 16.57964 0.093853 4.612872 16.60936 0.093853 4.557989 16.6406 0.093853 4.463515 16.67278 0.093853 4.322426 16.68183 0.093853 4.142715 16.60389 0.093853 3.982838 16.42385 0.093853 3.812994 16.17776 0.093853 3.610426 15.88346 0.093853 3.373845 15.54006 0.093853 3.102303 15.14738 0.093853 2.79515 14.70592 0.093853 2.451998 14.21694 0.093853 2.072593 13.6824 0.093853 1.656729 13.10503 0.093853 1.205339 12.4875 0.093853 0.718954 11.8334 0.093853 0.197118 11.14775 0.093853 −0.35942 10.43529 0.093853 −0.94963 9.701111 0.093853 −1.57258 8.950932 0.093853 −2.22687 8.19058 0.093853 −2.90975 7.425172 0.093853 −3.62067 6.662207 0.093853 −4.35809 5.90878 0.093853 −5.11886 5.170885 0.093853 −5.90236 4.457501 0.093853 −6.70739 3.777889 0.093853 −7.53201 3.141429 0.093853 −8.37296 2.557006 0.093853 −9.22544 2.032433 0.093853 −10.0826 1.573284 0.093853 −10.9368 1.183829 0.093853 −11.78 0.868251 0.093853 −12.6033 0.629317 0.093853 −13.3964 0.464458 0.093853 −14.1496 0.367814 0.093853 −14.854 0.330802 0.093853 −15.5021 0.341898 0.093853 −16.0899 0.387403 0.093853 −16.6149 0.453001 0.093853 −17.0774 0.523571 0.093853 −17.4793 0.584175 0.093853 −17.8226 0.625064 0.093853 −18.1088 0.632813 0.093853 −18.3356 0.596837 0.093853 −18.4926 0.51709 0.093853 −18.5768 0.423647 0.093853 −18.7453 −0.26494 0.150694 −18.7582 −0.32389 0.150694 −18.7631 −0.41141 0.150694 −18.7378 −0.54361 0.150694 −18.6453 −0.70838 0.150694 −18.4702 −0.88181 0.150694 −18.2148 −1.0527 0.150694 −17.882 −1.21639 0.150694 −17.4739 −1.37006 0.150694 −16.9918 −1.50971 0.150694 −16.4369 −1.629 0.150694 −15.8109 −1.71898 0.150694 −15.1171 −1.76954 0.150694 −14.3606 −1.76994 0.150694 −13.5482 −1.70983 0.150694 −12.6888 −1.5798 0.150694 −11.7928 −1.37266 0.150694 −10.8714 −1.08293 0.150694 −9.93678 −0.70784 0.150694 −9.00012 −0.24857 0.150694 −8.07214 0.291662 0.150694 −7.16264 0.90789 0.150694 −6.27947 1.592517 0.150694 −5.42823 2.335986 0.150694 −4.61298 3.128132 0.150694 −3.83703 3.959158 0.150694 −3.10105 4.81787 0.150694 −2.40471 5.69346 0.150694 −1.74726 6.575857 0.150694 −1.12908 7.45668 0.150694 −0.54915 8.327273 0.150694 −0.00344 9.177812 0.150694 0.5081 10.00179 0.150694 0.986121 10.79294 0.150694 1.432055 11.54513 0.150694 1.846798 12.25319 0.150694 2.230525 12.91306 0.150694 2.583442 13.52129 0.150694 2.905516 14.07533 0.150694 3.196599 14.57346 0.150694 3.456259 15.01494 0.150694 3.684301 15.3998 0.150694 3.880926 15.7288 0.150694 4.046505 16.0036 0.150694 4.181755 16.22676 0.150694 4.286798 16.4025 0.150694 4.331408 16.54817 0.150694 4.305824 16.6529 0.150694 4.270882 16.71025 0.150694 4.233954 16.7464 0.150694 4.192819 16.77193 0.150694 4.132294 16.78957 0.150694 4.03324 16.77595 0.150694 3.927272 16.68024 0.150694 3.818335 16.52257 0.150694 3.679538 16.32137 0.150694 3.508858 16.07402 0.150694 3.304824 15.77862 0.150694 3.066418 15.43402 0.150694 2.792984 15.03982 0.150694 2.484255 14.59627 0.150694 2.140308 14.10429 0.150694 1.761269 13.56559 0.150694 1.347596 12.9824 0.150694 0.900141 12.35742 0.150694 0.419685 11.69406 0.150694 −0.09299 10.99632 0.150694 −0.63687 10.26866 0.150694 −1.21097 9.516039 0.150694 −1.81469 8.744265 0.150694 −2.44714 7.959387 0.150694 −3.10748 7.167946 0.150694 −3.79543 6.377482 0.150694 −4.51046 5.595822 0.150694 −5.25283 4.832212 0.150694 −6.02015 4.09402 0.150694 −6.81206 3.391452 0.150694 −7.62642 2.733852 0.150694 −8.45967 2.130003 0.150694 −9.30707 1.588192 0.150694 −10.162 1.114947 0.150694 −11.0165 0.715344 0.150694 −11.8617 0.392809 0.150694 −12.6876 0.147933 0.150694 −13.4837 −0.02244 0.150694 −14.2398 −0.12468 0.150694 −14.9473 −0.16742 0.150694 −15.5988 −0.16265 0.150694 −16.1899 −0.12419 0.150694 −16.7184 −0.06669 0.150694 −17.1845 −0.00493 0.150694 −17.5896 0.046995 0.150694 −17.9354 0.07975 0.150694 −18.2232 0.080446 0.150694 −18.4503 0.039382 0.150694 −18.6069 −0.04332 0.150694 −18.6901 −0.13846 0.150694 −18.7891 −1.32355 0.181022 −18.7988 −1.38367 0.181022 −18.7987 −1.47212 0.181022 −18.7649 −1.60375 0.181022 −18.6613 −1.76376 0.181022 −18.4743 −1.92775 0.181022 −18.2066 −2.08449 0.181022 −17.8617 −2.22984 0.181022 −17.4417 −2.36145 0.181022 −16.9482 −2.47546 0.181022 −16.3825 −2.56576 0.181022 −15.7468 −2.62362 0.181022 −15.0449 −2.63913 0.181022 −14.2825 −2.6016 0.181022 −13.4664 −2.50049 0.181022 −12.6066 −2.32655 0.181022 −11.7138 −2.07287 0.181022 −10.7993 −1.73518 0.181022 −9.87546 −1.31132 0.181022 −8.95422 −0.80152 0.181022 −8.04691 −0.20878 0.181022 −7.16317 0.460898 0.181022 −6.31052 1.199154 0.181022 −5.49417 1.995865 0.181022 −4.7177 2.840456 0.181022 −3.98319 3.722107 0.181022 −3.29111 4.629804 0.181022 −2.6408 5.552835 0.181022 −2.03078 6.480903 0.181022 −1.45969 7.404717 0.181022 −0.92565 8.315467 0.181022 −0.42622 9.204744 0.181022 0.040313 10.06527 0.181022 0.475171 10.89064 0.181022 0.879933 11.6749 0.181022 1.255879 12.41286 0.181022 1.603239 13.10052 0.181022 1.922345 13.73447 0.181022 2.213514 14.31202 0.181022 2.476445 14.83157 0.181022 2.711112 15.29216 0.181022 2.917251 15.69385 0.181022 3.095114 16.03737 0.181022 3.245017 16.3244 0.181022 3.367606 16.55749 0.181022 3.463354 16.74052 0.181022 3.502366 16.88947 0.181022 3.472946 16.99389 0.181022 3.434927 17.05006 0.181022 3.395753 17.08451 0.181022 3.35273 17.10773 0.181022 3.290597 17.1213 0.181022 3.192027 17.09874 0.181022 3.093553 16.99372 0.181022 2.992759 16.82858 0.181022 2.86429 16.61789 0.181022 2.706372 16.35884 0.181022 2.517672 16.04939 0.181022 2.297319 15.68828 0.181022 2.044739 15.27502 0.181022 1.759735 14.8098 0.181022 1.442404 14.29352 0.181022 1.092809 13.72784 0.181022 0.711333 13.11505 0.181022 0.298647 12.4579 0.181022 −0.14481 11.75996 0.181022 −0.61863 11.02542 0.181022 −1.12205 10.2588 0.181022 −1.65449 9.465255 0.181022 −2.21593 8.650811 0.181022 −2.80593 7.821691 0.181022 −3.42413 6.984657 0.181022 −4.07083 6.147416 0.181022 −4.74612 5.318089 0.181022 −5.45006 4.505405 0.181022 −6.18182 3.718015 0.181022 −6.94098 2.965735 0.181022 −7.72622 2.258599 0.181022 −8.53463 1.606091 0.181022 −9.36156 1.01679 0.181022 −10.2005 0.497778 0.181022 −11.0432 0.054061 0.181022 −11.88 −0.31177 0.181022 −12.7009 −0.59898 0.181022 −13.4954 −0.80967 0.181022 −14.2528 −0.94956 0.181022 −14.9642 −1.0273 0.181022 −15.6212 −1.05498 0.181022 −16.2192 −1.04655 0.181022 −16.7552 −1.01657 0.181022 −17.2283 −0.97945 0.181022 −17.6395 −0.94861 0.181022 −17.9899 −0.93452 0.181022 −18.28 −0.94927 0.181022 −18.5067 −1.00247 0.181022 −18.6605 −1.09331 0.181022 −18.74 −1.19315 0.181022 −19.2256 −1.74087 0.283392 −19.2339 −1.80326 0.283392 −19.2305 −1.89452 0.283392 −19.1896 −2.02891 0.283392 −19.0746 −2.18886 0.283392 −18.874 −2.34944 0.283392 −18.5913 −2.50036 0.283392 −18.23 −2.63837 0.283392 −17.7923 −2.76156 0.283392 −17.2796 −2.86669 0.283392 −16.6933 −2.94827 0.283392 −16.0357 −2.99846 0.283392 −15.3105 −3.00781 0.283392 −14.5228 −2.96579 0.283392 −13.6796 −2.86146 0.283392 −12.7907 −2.68453 0.283392 −11.867 −2.42668 0.283392 −10.9206 −2.08224 0.283392 −9.96436 −1.64791 0.283392 −9.01122 −1.12354 0.283392 −8.07337 −0.51178 0.283392 −7.16136 0.181533 0.283392 −6.28356 0.947915 0.283392 −5.44584 1.776897 0.283392 −4.65202 2.657181 0.283392 −3.90434 3.577322 0.283392 −3.20329 4.525674 0.283392 −2.54771 5.490634 0.283392 −1.93545 6.461118 0.283392 −1.36469 7.427265 0.283392 −0.83342 8.379975 0.283392 −0.33845 9.310289 0.283392 0.122676 10.21041 0.283392 0.551411 11.07371 0.283392 0.94939 11.89413 0.283392 1.318532 12.66612 0.283392 1.659355 13.38545 0.283392 1.972103 14.04871 0.283392 2.257488 14.65298 0.283392 2.515047 15.19669 0.283392 2.745002 15.67875 0.283392 2.947012 16.09923 0.283392 3.12134 16.45889 0.283392 3.26826 16.75946 0.283392 3.388485 17.00358 0.283392 3.482812 17.19498 0.283392 3.522562 17.34916 0.283392 3.492472 17.45679 0.283392 3.452435 17.51439 0.283392 3.411172 17.54908 0.283392 3.365797 17.57152 0.283392 3.301052 17.58252 0.283392 3.200511 17.55146 0.283392 3.105917 17.43722 0.283392 3.005737 17.26393 0.283392 2.878179 17.04278 0.283392 2.721506 16.7708 0.283392 2.534445 16.44581 0.283392 2.31621 16.06644 0.283392 2.066287 15.63213 0.283392 1.784538 15.14304 0.283392 1.471052 14.60007 0.283392 1.125806 14.00499 0.283392 0.749197 13.36011 0.283392 0.341729 12.66838 0.283392 −0.09651 11.93365 0.283392 −0.56536 11.16036 0.283392 −1.06427 10.35325 0.283392 −1.59323 9.517994 0.283392 −2.15289 8.66116 0.283392 −2.74307 7.789333 0.283392 −3.36402 6.909898 0.283392 −4.01666 6.031267 0.283392 −4.70182 5.16247 0.283392 −5.41958 4.312685 0.283392 −6.16937 3.491365 0.283392 −6.95073 2.709015 0.283392 −7.76194 1.976128 0.283392 −8.59944 1.302481 0.283392 −9.45777 0.696791 0.283392 −10.3294 0.165915 0.283392 −11.2052 −0.28553 0.283392 −12.0748 −0.65517 0.283392 −12.9272 −0.94349 0.283392 −13.751 −1.15418 0.283392 −14.5356 −1.29403 0.283392 −15.2716 −1.37341 0.283392 −15.9513 −1.40498 0.283392 −16.5701 −1.40274 0.283392 −17.125 −1.38029 0.283392 −17.6152 −1.35209 0.283392 −18.0412 −1.33019 0.283392 −18.404 −1.32501 0.283392 −18.7037 −1.34741 0.283392 −18.9375 −1.40606 0.283392 −19.0961 −1.50106 0.283392 −19.1776 −1.60502 0.283392 −19.9766 −1.51874 0.385762 −19.9836 −1.58337 0.385762 −19.9775 −1.67714 0.385762 −19.9323 −1.81445 0.385762 −19.8138 −1.97951 0.385762 −19.6038 −2.1423 0.385762 −19.3096 −2.29483 0.385762 −18.9346 −2.43366 0.385762 −18.4813 −2.55848 0.385762 −17.9508 −2.66536 0.385762 −17.3446 −2.74949 0.385762 −16.665 −2.80604 0.385762 −15.9153 −2.82614 0.385762 −15.1 −2.7995 0.385762 −14.2257 −2.71478 0.385762 −13.3013 −2.5612 0.385762 −12.3371 −2.32947 0.385762 −11.3451 −2.01266 0.385762 −10.3381 −1.6065 0.385762 −9.32909 −1.10933 0.385762 −8.33134 −0.52202 0.385762 −7.35688 0.151413 0.385762 −6.41608 0.904116 0.385762 −5.51659 1.726207 0.385762 −4.66301 2.605713 0.385762 −3.85771 3.529977 0.385762 −3.1019 4.48689 0.385762 −2.39494 5.464219 0.385762 −1.73507 6.450243 0.385762 −1.12037 7.434295 0.385762 −0.54849 8.406433 0.385762 −0.0168 9.357482 0.385762 0.47795 10.27875 0.385762 0.937378 11.16317 0.385762 1.363055 12.00444 0.385762 1.757269 12.79653 0.385762 2.120862 13.53488 0.385762 2.454116 14.21592 0.385762 2.757895 14.83654 0.385762 3.031731 15.39508 0.385762 3.276035 15.89034 0.385762 3.490482 16.32238 0.385762 3.675406 16.69194 0.385762 3.83116 17.00082 0.385762 3.958555 17.25168 0.385762 4.058751 17.44823 0.385762 4.105215 17.60628 0.385762 4.078813 17.71837 0.385762 4.039021 17.77916 0.385762 3.997023 17.81581 0.385762 3.950089 17.83932 0.385762 3.883148 17.8506 0.385762 3.77931 17.81515 0.385762 3.683992 17.6954 0.385762 3.577766 17.51732 0.385762 3.442709 17.28992 0.385762 3.276841 17.01024 0.385762 3.078825 16.67605 0.385762 2.84781 16.28592 0.385762 2.583286 15.83928 0.385762 2.285048 15.33633 0.385762 1.953136 14.77803 0.385762 1.587432 14.1663 0.385762 1.188332 13.50355 0.385762 0.756146 12.79299 0.385762 0.290696 12.0388 0.385762 −0.20799 11.24572 0.385762 −0.73951 10.41885 0.385762 −1.30432 9.564461 0.385762 −1.90299 8.689452 0.385762 −2.53575 7.801112 0.385762 −3.20303 6.907485 0.385762 −3.9056 6.017536 0.385762 −4.64401 5.140811 0.385762 −5.41831 4.287366 0.385762 −6.22797 3.467764 0.385762 −7.07188 2.693224 0.385762 −7.94692 1.974191 0.385762 −8.84795 1.320041 0.385762 −9.76779 0.738412 0.385762 −10.6974 0.234772 0.385762 −11.6267 −0.18765 0.385762 −12.5445 −0.52784 0.385762 −13.4396 −0.78743 0.385762 −14.3011 −0.97144 0.385762 −15.1183 −1.08846 0.385762 −15.8826 −1.14984 0.385762 −16.5873 −1.16821 0.385762 −17.2282 −1.15776 0.385762 −17.8028 −1.13132 0.385762 −18.3107 −1.10248 0.385762 −18.7522 −1.08212 0.385762 −19.1282 −1.08127 0.385762 −19.4394 −1.10361 0.385762 −19.6809 −1.16969 0.385762 −19.8408 −1.27396 0.385762 −19.9254 −1.37943 0.385762 −21.0083 −0.66329 0.488132 −21.0153 −0.73014 0.488132 −21.0081 −0.82694 0.488132 −20.961 −0.96912 0.488132 −20.8366 −1.13863 0.488132 −20.6216 −1.31006 0.488132 −20.3177 −1.46991 0.488132 −19.9303 −1.6165 0.488132 −19.462 −1.74909 0.488132 −18.9146 −1.86634 0.488132 −18.2896 −1.96636 0.488132 −17.5885 −2.04421 0.488132 −16.8142 −2.09193 0.488132 −15.9706 −2.10046 0.488132 −15.0631 −2.05979 0.488132 −14.0991 −1.95881 0.488132 −13.088 −1.78671 0.488132 −12.0412 −1.53331 0.488132 −10.9713 −1.19149 0.488132 −9.89168 −0.75797 0.488132 −8.81525 −0.23318 0.488132 −7.75408 0.379303 0.488132 −6.7193 1.073846 0.488132 −5.72082 1.843101 0.488132 −4.76677 2.677875 0.488132 −3.86343 3.56768 0.488132 −3.01222 4.498398 0.488132 −2.2132 5.456622 0.488132 −1.46536 6.42963 0.488132 −0.76707 7.405653 0.488132 −0.11622 8.373815 0.488132 0.489732 9.324039 0.488132 1.053669 10.24699 0.488132 1.577887 11.1346 0.488132 2.063468 11.9803 0.488132 2.512693 12.77759 0.488132 2.926717 13.5214 0.488132 3.305628 14.20802 0.488132 3.65059 14.83394 0.488132 3.961035 15.3975 0.488132 4.23758 15.89729 0.488132 4.480027 16.33331 0.488132 4.688823 16.70627 0.488132 4.864496 17.01798 0.488132 5.00807 17.27111 0.488132 5.121085 17.46933 0.488132 5.179706 17.62942 0.488132 5.161282 17.74669 0.488132 5.124075 17.81214 0.488132 5.082767 17.85237 0.488132 5.035184 17.8788 0.488132 4.966309 17.89284 0.488132 4.858169 17.85663 0.488132 4.756634 17.73495 0.488132 4.638252 17.55547 0.488132 4.487773 17.3262 0.488132 4.302867 17.04425 0.488132 4.082005 16.7074 0.488132 3.824181 16.31427 0.488132 3.528697 15.86436 0.488132 3.195248 15.35796 0.488132 2.823731 14.79621 0.488132 2.413958 14.18119 0.488132 1.966305 13.51551 0.488132 1.480994 12.80263 0.488132 0.957797 12.04713 0.488132 0.396855 11.25402 0.488132 −0.20143 10.42882 0.488132 −0.83765 9.578452 0.488132 −1.51245 8.710552 0.488132 −2.22616 7.833263 0.488132 −2.97866 6.955116 0.488132 −3.77089 6.086376 0.488132 −4.60327 5.237912 0.488132 −5.47485 4.420501 0.488132 −6.3833 3.644674 0.488132 −7.32484 2.920524 0.488132 −8.29393 2.257104 0.488132 −9.2836 1.662403 0.488132 −10.2855 1.142965 0.488132 −11.2898 0.703406 0.488132 −12.286 0.345989 0.488132 −13.2627 0.070201 0.488132 −14.2083 −0.12881 0.488132 −15.1123 −0.25875 0.488132 −15.9653 −0.33029 0.488132 −16.7599 −0.35582 0.488132 −17.4908 −0.34801 0.488132 −18.1547 −0.31897 0.488132 −18.7499 −0.28032 0.488132 −19.276 −0.24268 0.488132 −19.7337 −0.21636 0.488132 −20.1239 −0.21104 0.488132 −20.4464 −0.23954 0.488132 −20.6968 −0.30734 0.488132 −20.8652 −0.41107 0.488132 −20.9543 −0.5193 0.488132 −22.8112 −0.94945 0.590502 −22.8154 −1.02001 0.590502 −22.8061 −1.12174 0.590502 −22.76 −1.27134 0.590502 −22.6417 −1.458 0.590502 −22.4239 −1.6522 0.590502 −22.1027 −1.82764 0.590502 −21.6877 −1.96966 0.590502 −21.1841 −2.07772 0.590502 −20.5986 −2.15685 0.590502 −19.9342 −2.21334 0.590502 −19.1925 −2.25006 0.590502 −18.376 −2.26739 0.590502 −17.4878 −2.25902 0.590502 −16.5326 −2.21457 0.590502 −15.5168 −2.12009 0.590502 −14.4489 −1.96319 0.590502 −13.3383 −1.73549 0.590502 −12.1961 −1.42981 0.590502 −11.0347 −1.04056 0.590502 −9.86891 −0.5612 0.590502 −8.7145 0.0132 0.590502 −7.58717 0.683734 0.590502 −6.4994 1.4433 0.590502 −5.45814 2.277878 0.590502 −4.46741 3.17239 0.590502 −3.53209 4.114778 0.590502 −2.65645 5.093723 0.590502 −1.83997 6.094874 0.590502 −1.08003 7.10411 0.590502 −0.37473 8.109486 0.590502 0.278341 9.099949 0.590502 0.882934 10.06478 0.590502 1.441932 10.9949 0.590502 1.957155 11.88283 0.590502 2.431592 12.72127 0.590502 2.867429 13.50428 0.590502 3.265156 14.22771 0.590502 3.626397 14.88766 0.590502 3.951023 15.48211 0.590502 4.239734 16.00955 0.590502 4.492622 16.46984 0.590502 4.710214 16.86369 0.590502 4.893207 17.1929 0.590502 5.042738 17.46028 0.590502 5.160426 17.66965 0.590502 5.225781 17.83696 0.590502 5.211507 17.96034 0.590502 5.17347 18.03014 0.590502 5.13029 18.07279 0.590502 5.079715 18.10034 0.590502 5.006767 18.11351 0.590502 4.89463 18.0679 0.590502 4.792094 17.93575 0.590502 4.66852 17.74489 0.590502 4.511416 17.50112 0.590502 4.318221 17.20144 0.590502 4.08714 16.84361 0.590502 3.816986 16.42626 0.590502 3.506885 15.94894 0.590502 3.156291 15.4121 0.590502 2.764791 14.81715 0.590502 2.331968 14.16644 0.590502 1.857857 13.46297 0.590502 1.342101 12.71085 0.590502 0.783849 11.91538 0.590502 0.182822 11.08228 0.590502 −0.46127 10.21803 0.590502 −1.14977 9.330744 0.590502 −1.88322 8.428742 0.590502 −2.66144 7.520648 0.590502 −3.48624 6.617723 0.590502 −4.35725 5.73048 0.590502 −5.27241 4.8689 0.590502 −6.2297 4.044055 0.590502 −7.22634 3.267791 0.590502 −8.25909 2.552894 0.590502 −9.32273 1.911931 0.590502 −10.4075 1.351923 0.590502 −11.5016 0.875604 0.590502 −12.592 0.481382 0.590502 −13.666 0.165488 0.590502 −14.7124 −0.07442 0.590502 −15.7207 −0.24144 0.590502 −16.6814 −0.33948 0.590502 −17.5855 −0.37747 0.590502 −18.4259 −0.36944 0.590502 −19.1979 −0.33225 0.590502 −19.899 −0.28385 0.590502 −20.5286 −0.241 0.590502 −21.0865 −0.21893 0.590502 −21.5714 −0.23095 0.590502 −21.9804 −0.28585 0.590502 −22.3059 −0.38791 0.590502 −22.5434 −0.5206 0.590502 −22.6909 −0.66515 0.590502 −22.7669 −0.79218 0.590502 −26.3511 −3.44707 0.69289 −26.3523 −3.5263 0.69289 −26.3452 −3.64135 0.69289 −26.3161 −3.81613 0.69289 −26.2441 −4.04888 0.69289 −26.1026 −4.32841 0.69289 −25.8552 −4.63965 0.69289 −25.4701 −4.94085 0.69289 −24.9417 −5.1771 0.69289 −24.2855 −5.30742 0.69289 −23.5336 −5.35192 0.69289 −22.7 −5.32166 0.69289 −21.7911 −5.22581 0.69289 −20.8104 −5.06962 0.69289 −19.7643 −4.85385 0.69289 −18.6588 −4.57944 0.69289 −17.5005 −4.2464 0.69289 −16.2957 −3.85768 0.69289 −15.0515 −3.41601 0.69289 −13.7757 −2.92271 0.69289 −12.4796 −2.37328 0.69289 −11.1798 −1.75597 0.69289 −9.89316 −1.06115 0.69289 −8.63824 −0.27973 0.69289 −7.43146 0.589959 0.69289 −6.29031 1.546214 0.69289 −5.22538 2.576847 0.69289 −4.24117 3.663793 0.69289 −3.33792 4.788164 0.69289 −2.51225 5.931543 0.69289 −1.75999 7.077691 0.69289 −1.07614 8.211891 0.69289 −0.4543 9.320457 0.69289 0.111028 10.39187 0.69289 0.624468 11.41641 0.69289 1.090179 12.38576 0.69289 1.512841 13.29247 0.69289 1.895367 14.13092 0.69289 2.240101 14.89678 0.69289 2.548674 15.58706 0.69289 2.822313 16.2 0.69289 3.061592 16.73522 0.69289 3.267366 17.19344 0.69289 3.440512 17.57661 0.69289 3.582092 17.88791 0.69289 3.693064 18.13199 0.69289 3.760106 18.32125 0.69289 3.747693 18.4579 0.69289 3.702051 18.53465 0.69289 3.651136 18.57928 0.69289 3.591847 18.60489 0.69289 3.509496 18.60946 0.69289 3.395996 18.53419 0.69289 3.301135 18.37253 0.69289 3.181809 18.14752 0.69289 3.030005 17.86032 0.69289 2.84298 17.50741 0.69289 2.618607 17.08632 0.69289 2.355464 16.5955 0.69289 2.052247 16.03461 0.69289 1.707769 15.40439 0.69289 1.320727 14.70677 0.69289 0.889878 13.94472 0.69289 0.413915 13.12226 0.69289 −0.10933 12.24489 0.69289 −0.68163 11.31888 0.69289 −1.30496 10.3516 0.69289 −1.98142 9.35151 0.69289 −2.71338 8.328335 0.69289 −3.50322 7.292952 0.69289 −4.35291 6.257261 0.69289 −5.26375 5.234062 0.69289 −6.23629 4.23708 0.69289 −7.2705 3.282117 0.69289 −8.36541 2.385753 0.69289 −9.51838 1.565571 0.69289 −10.7231 0.838889 0.69289 −11.9688 0.220226 0.69289 −13.241 −0.27926 0.69289 −14.5228 −0.65576 0.69289 −15.7958 −0.91281 0.69289 −17.0399 −1.06898 0.69289 −18.2399 −1.14476 0.69289 −19.3845 −1.16278 0.69289 −20.4662 −1.14402 0.69289 −21.4796 −1.11125 0.69289 −22.4215 −1.08569 0.69289 −23.2879 −1.09072 0.69289 −24.0751 −1.15754 0.69289 −24.7688 −1.3134 0.69289 −25.3432 −1.56382 0.69289 −25.771 −1.8923 0.69289 −26.0514 −2.24918 0.69289 −26.2118 −2.58394 0.69289 −26.2914 −2.86884 0.69289 −26.3258 −3.09644 0.69289 −26.3398 −3.26309 0.69289 −30.3275 −2.64888 0.79526 −30.3181 −3.18617 0.79526 −30.2475 −3.6763 0.79526 −30.1157 −4.11927 0.79526 −29.9228 −4.51509 0.79526 −29.6688 −4.86375 0.79526 −29.3535 −5.16526 0.79526 −28.9771 −5.41961 0.79526 −28.5397 −5.62732 0.79526 −28.0411 −5.78801 0.79526 −27.4815 −5.90375 0.79526 −26.8605 −5.97476 0.79526 −26.1773 −6.00073 0.79526 −25.0677 −5.94955 0.79526 −23.8811 −5.79882 0.79526 −22.6295 −5.55653 0.79526 −21.32 −5.232 0.79526 −19.9604 −4.83287 0.79526 −18.5586 −4.36665 0.79526 −17.1235 −3.83632 0.79526 −15.6643 −3.24382 0.79526 −14.1908 −2.59129 0.79526 −12.7137 −1.88063 0.79526 −11.246 −1.11023 0.79526 −9.803 −0.27528 0.79526 −8.40072 0.62718 0.79526 −7.05506 1.596611 0.79526 −5.78329 2.632103 0.79526 −4.59997 3.727854 0.79526 −3.51439 4.872104 0.79526 −2.52887 6.047319 0.79526 −1.63911 7.232453 0.79526 −0.83737 8.407377 0.79526 −0.11525 9.554738 0.79526 0.535486 10.65989 0.79526 1.122013 11.71084 0.79526 1.650563 12.69776 0.79526 2.126174 13.61292 0.79526 2.552562 14.45056 0.79526 2.932457 15.20667 0.79526 3.268127 15.8787 0.79526 3.561045 16.4658 0.79526 3.812208 16.96871 0.79526 4.023189 17.38931 0.79526 4.195509 17.73105 0.79526 4.330476 17.99901 0.79526 4.42135 18.20459 0.79526 4.430326 18.35754 0.79526 4.386766 18.44794 0.79526 4.33333 18.50155 0.79526 4.267625 18.53282 0.79526 4.175679 18.53667 0.79526 4.054276 18.44327 0.79526 3.944836 18.26179 0.79526 3.801899 18.01337 0.79526 3.619582 17.69652 0.79526 3.394088 17.30773 0.79526 3.122774 16.8444 0.79526 2.803456 16.30517 0.79526 2.434069 15.69005 0.79526 2.012728 15.00035 0.79526 1.537417 14.23873 0.79526 1.006163 13.40915 0.79526 0.416098 12.51736 0.79526 −0.23622 11.57083 0.79526 −0.95407 10.57824 0.79526 −1.74095 9.549855 0.79526 −2.60033 8.4975 0.79526 −3.53698 7.435941 0.79526 −4.55561 6.382427 0.79526 −5.66 5.356348 0.79526 −6.85221 4.379065 0.79526 −8.13156 3.473722 0.79526 −9.49249 2.663417 0.79526 −10.9238 1.968543 0.79526 −12.4097 1.402782 0.79526 −13.9316 0.971558 0.79526 −15.4682 0.670962 0.79526 −16.998 0.491269 0.79526 −18.5012 0.418464 0.79526 −19.9591 0.434118 0.79526 −21.3609 0.518972 0.79526 −22.7064 0.644195 0.79526 −23.9878 0.776605 0.79526 −25.2016 0.877264 0.79526 −25.8891 0.900231 0.79526 −26.5263 0.887592 0.79526 −27.1141 0.834345 0.79526 −27.6527 0.737393 0.79526 −28.142 0.596642 0.79526 −28.5818 0.411473 0.79526 −28.9723 0.182429 0.79526 −29.3136 −0.0902 0.79526 −29.6059 −0.40667 0.79526 −29.8489 −0.76709 0.79526 −30.0425 −1.17162 0.79526 −30.1867 −1.62009 0.79526 −34.1652 −3.66374 0.89763 −34.1557 −4.34915 0.89763 −34.0789 −4.97484 0.89763 −33.9347 −5.5408 0.89763 −33.7231 −6.04705 0.89763 −33.4442 −6.49357 0.89763 −33.0979 −6.88037 0.89763 −32.6843 −7.20746 0.89763 −32.2033 −7.47482 0.89763 −31.655 −7.68246 0.89763 −31.0393 −7.83039 0.89763 −30.3562 −7.91859 0.89763 −29.6058 −7.94821 0.89763 −28.7877 −7.92052 0.89763 −27.9015 −7.83523 0.89763 −26.5064 −7.60215 0.89763 −25.0493 −7.25543 0.89763 −23.5423 −6.805 0.89763 −21.9958 −6.26196 0.89763 −20.4186 −5.63805 0.89763 −18.8169 −4.94434 0.89763 −17.1989 −4.1878 0.89763 −15.5727 −3.37424 0.89763 −13.9496 −2.50842 0.89763 −12.3426 −1.59167 0.89763 −10.764 −0.62625 0.89763 −9.22945 0.389607 0.89763 −7.75628 1.45735 0.89763 −6.36231 2.5772 0.89763 −5.06524 3.748464 0.89763 −3.87634 4.96214 0.89763 −2.80034 6.202559 0.89763 −1.83675 7.450356 0.89763 −0.97793 8.68363 0.89763 −0.21398 9.882757 0.89763 0.466246 11.03062 0.89763 1.072271 12.11379 0.89763 1.611804 13.12193 0.89763 2.09118 14.04716 0.89763 2.515131 14.88402 0.89763 2.886842 15.62928 0.89763 3.20999 16.28097 0.89763 3.486388 16.83954 0.89763 3.717852 17.30707 0.89763 3.907392 17.68669 0.89763 4.057032 17.9838 0.89763 4.162282 18.20941 0.89763 4.187847 18.37802 0.89763 4.144059 18.48006 0.89763 4.086277 18.54094 0.89763 4.012402 18.57557 0.89763 3.909838 18.57276 0.89763 3.785241 18.45569 0.89763 3.664859 18.24985 0.89763 3.506793 17.97026 0.89763 3.30546 17.6135 0.89763 3.056351 17.17576 0.89763 2.754951 16.65501 0.89763 2.398266 16.05006 0.89763 1.982688 15.36175 0.89763 1.504841 14.59236 0.89763 0.961263 13.74582 0.89763 0.348109 12.82784 0.89763 −0.33882 11.84599 0.89763 −1.10398 10.80966 0.89763 −1.95209 9.730172 0.89763 −2.88797 8.621032 0.89763 −3.91769 7.499243 0.89763 −5.04867 6.386821 0.89763 −6.28783 5.310014 0.89763 −7.64063 4.299192 0.89763 −9.10642 3.386182 0.89763 −10.6747 2.599408 0.89763 −12.3274 1.960858 0.89763 −14.0417 1.47896 0.89763 −15.7935 1.149946 0.89763 −17.5577 0.962438 0.89763 −19.3122 0.899023 0.89763 −21.0362 0.938397 0.89763 −22.7076 1.054666 0.89763 −24.3192 1.215202 0.89763 −25.8801 1.384676 0.89763 −26.808 1.470601 0.89763 −27.6772 1.529525 0.89763 −28.49 1.550705 0.89763 −29.2481 1.526394 0.89763 −29.9522 1.449993 0.89763 −30.6021 1.3192 0.89763 −31.1975 1.133938 0.89763 −31.7385 0.894885 0.89763 −32.2254 0.602597 0.89763 −32.6579 0.256749 0.89763 −33.0361 −0.14265 0.89763 −33.36 −0.59561 0.89763 −33.6297 −1.10213 0.89763 −33.845 −1.6622 0.89763 −34.006 −2.27582 0.89763 −38.0991 −2.78081 1 −38.1379 −3.69733 1 −38.1014 −4.53751 1 −37.9897 −5.30135 1 −37.8028 −5.98884 1 −37.5406 −6.6 1 −37.2032 −7.13481 1 −36.7905 −7.59328 1 −36.3025 −7.97541 1 −35.7393 −8.28121 1 −35.1009 −8.51066 1 −34.3872 −8.66376 1 −33.5982 −8.74053 1 −32.734 −8.74132 1 −31.7938 −8.67206 1 −30.776 −8.5342 1 −29.163 −8.20884 1 −27.4927 −7.76738 1 −25.7761 −7.22254 1 −24.0266 −6.58308 1 −22.2536 −5.85842 1 −20.4649 −5.05877 1 −18.6631 −4.19736 1 −16.8579 −3.29065 1 −15.0566 −2.35035 1 −13.2693 −1.38233 1 −11.5101 −0.38519 1 −9.79759 0.647919 1 −8.15326 1.726413 1 −6.60103 2.860401 1 −5.16302 4.053266 1 −3.85112 5.293396 1 −2.66988 6.561533 1 −1.61517 7.83289 1 −0.67653 9.082232 1 0.156754 10.2889 1 0.895415 11.43571 1 1.548932 12.50908 1 2.126724 13.4979 1 2.635685 14.39456 1 3.080336 15.1946 1 3.465546 15.89513 1 3.794656 16.49583 1 4.069947 16.99878 1 4.294623 17.40742 1 4.471288 17.72752 1 4.597431 17.9699 1 4.645259 18.15292 1 4.609418 18.26849 1 4.550551 18.33971 1 4.469946 18.38166 1 4.356222 18.37402 1 4.22256 18.23964 1 4.082986 18.01287 1 3.897494 17.70711 1 3.659466 17.31801 1 3.363096 16.84191 1 3.003858 16.27641 1 2.576922 15.62129 1 2.077473 14.87829 1 1.500827 14.05095 1 0.841903 13.14506 1 0.095045 12.16879 1 −0.7455 11.13255 1 −1.68524 10.04887 1 −2.72986 8.932966 1 −3.88512 7.803113 1 −5.15782 6.683304 1 −6.55494 5.604793 1 −8.08023 4.602268 1 −9.73271 3.713931 1 −11.5004 2.97238 1 −13.3613 2.401445 1 −15.2906 2.010997 1 −17.2636 1.798026 1 −19.2516 1.750351 1 −21.2286 1.845253 1 −23.1707 2.056238 1 −25.062 2.355102 1 −26.8813 2.706436 1 −28.6444 3.074309 1 −30.3633 3.417352 1 −31.1887 3.552601 1 −31.9591 3.64974 1 −32.68 3.701424 1 −33.3555 3.695211 1 −33.9868 3.61763 1 −34.5737 3.469158 1 −35.1162 3.250737 1 −35.6143 2.962363 1 −36.068 2.604038 1 −36.4772 2.175762 1 −36.8421 1.677534 1 −37.1626 1.109357 1 −37.4387 0.471225 1 −37.6704 −0.23686 1 −37.8577 −1.01489 1 −41.8307 −5.24889 1.10237 −41.7479 −6.31795 1.10237 −41.5992 −7.29602 1.10237 −41.3847 −8.18308 1.10237 −41.1045 −8.97916 1.10237 −40.7584 −9.68423 1.10237 −40.3465 −10.2983 1.10237 −39.8688 −10.8214 1.10237 −39.3252 −11.2535 1.10237 −38.7159 −11.5946 1.10237 −38.0407 −11.8447 1.10237 −37.2998 −12.0038 1.10237 −36.493 −12.0719 1.10237 −35.6204 −12.049 1.10237 −34.6805 −11.9451 1.10237 −33.67 −11.7667 1.10237 −32.585 −11.5144 1.10237 −30.7776 −10.9731 1.10237 −28.9306 −10.2939 1.10237 −27.0605 −9.49228 1.10237 −25.1766 −8.58897 1.10237 −23.2807 −7.60292 1.10237 −21.3723 −6.55308 1.10237 −19.4594 −5.46154 1.10237 −17.5467 −4.34613 1.10237 −15.639 −3.21808 1.10237 −13.7481 −2.08253 1.10237 −11.8931 −0.93287 1.10237 −10.0973 0.242452 1.10237 −8.38844 1.460152 1.10237 −6.79761 2.735849 1.10237 −5.34609 4.067554 1.10237 −4.04076 5.435701 1.10237 −2.88226 6.816509 1.10237 −1.86092 8.181942 1.10237 −0.96383 9.507059 1.10237 −0.17706 10.77067 1.10237 0.511258 11.95667 1.10237 1.114022 13.05139 1.10237 1.641552 14.04511 1.10237 2.10002 14.93245 1.10237 2.495311 15.71012 1.10237 2.832595 16.37711 1.10237 3.114444 16.93567 1.10237 3.34396 17.38984 1.10237 3.522677 17.74654 1.10237 3.650014 18.01585 1.10237 3.704023 18.21665 1.10237 3.669024 18.34255 1.10237 3.603965 18.41991 1.10237 3.513391 18.46345 1.10237 3.389463 18.44091 1.10237 3.256696 18.27978 1.10237 3.116067 18.02048 1.10237 2.926614 17.67335 1.10237 2.680191 17.23326 1.10237 2.370765 16.69583 1.10237 1.99415 16.05787 1.10237 1.543039 15.3202 1.10237 1.011623 14.48494 1.10237 0.393521 13.55675 1.10237 −0.31839 12.54304 1.10237 −1.13253 11.45464 1.10237 −2.05696 10.3048 1.10237 −3.0989 9.109064 1.10237 −4.26275 7.883243 1.10237 −5.55472 6.648328 1.10237 −6.982 5.432327 1.10237 −8.55511 4.275891 1.10237 −10.2837 3.229241 1.10237 −12.1661 2.346159 1.10237 −14.1789 1.667472 1.10237 −16.2869 1.210419 1.10237 −18.4564 0.971359 1.10237 −20.6547 0.922449 1.10237 −22.8536 1.0268 1.10237 −25.0256 1.249018 1.10237 −27.1553 1.561034 1.10237 −29.2292 1.936206 1.10237 −31.2337 2.336825 1.10237 −33.1918 2.713907 1.10237 −35.1142 3.002805 1.10237 −35.934 3.062686 1.10237 −36.6958 3.068858 1.10237 −37.4036 3.01526 1.10237 −38.0591 2.895473 1.10237 −38.6623 2.703886 1.10237 −39.2135 2.44054 1.10237 −39.7124 2.10458 1.10237 −40.1592 1.696003 1.10237 −40.5538 1.214813 1.10237 −40.8961 0.661004 1.10237 −41.1862 0.034581 1.10237 −41.4242 −0.66446 1.10237 −41.6099 −1.43611 1.10237 −41.7434 −2.28038 1.10237 −41.8252 −3.19725 1.10237 −45.6318 −6.74965 1.20474 −45.4623 −7.80926 1.20474 −45.2261 −8.7808 1.20474 −44.9233 −9.66428 1.20474 −44.5539 −10.4597 1.20474 −44.118 −11.167 1.20474 −43.6154 −11.7863 1.20474 −43.0463 −12.3175 1.20474 −42.4106 −12.7606 1.20474 −41.7083 −13.1157 1.20474 −40.9394 −13.3827 1.20474 −40.1039 −13.5616 1.20474 −39.2018 −13.6525 1.20474 −38.2331 −13.6556 1.20474 −37.1978 −13.5709 1.20474 −36.0952 −13.4011 1.20474 −34.9248 −13.1468 1.20474 −33.6863 −12.807 1.20474 −32.3799 −12.3795 1.20474 −30.3284 −11.5676 1.20474 −28.2775 −10.605 1.20474 −26.2294 −9.51845 1.20474 −24.1823 −8.3393 1.20474 −22.137 −7.10725 1.20474 −20.0908 −5.85747 1.20474 −18.0321 −4.62127 1.20474 −15.9798 −3.39446 1.20474 −13.9521 −2.17396 1.20474 −11.9752 −0.94443 1.20474 −10.0786 0.314068 1.20474 −8.29315 1.619442 1.20474 −6.65212 2.987269 1.20474 −5.17263 4.407428 1.20474 −3.85834 5.854655 1.20474 −2.70379 7.29948 1.20474 −1.69486 8.711801 1.20474 −0.81554 10.06597 1.20474 −0.05022 11.34135 1.20474 0.615507 12.52209 1.20474 1.195905 13.59553 1.20474 1.698594 14.55517 1.20474 2.13052 15.39705 1.20474 2.498661 16.11933 1.20474 2.806055 16.72433 1.20474 3.056026 17.21642 1.20474 3.24877 17.60388 1.20474 3.386361 17.89604 1.20474 3.452319 18.11283 1.20474 3.422555 18.25011 1.20474 3.353896 18.33597 1.20474 3.254594 18.38418 1.20474 3.120466 18.34985 1.20474 2.983548 18.16683 1.20474 2.833171 17.87945 1.20474 2.627798 17.49665 1.20474 2.35725 17.01315 1.20474 2.016005 16.4236 1.20474 1.599007 15.72479 1.20474 1.096931 14.91852 1.20474 0.50253 14.00787 1.20474 −0.19137 12.99839 1.20474 −0.99575 11.90097 1.20474 −1.92011 10.72855 1.20474 −2.97333 9.496813 1.20474 −4.16373 8.224401 1.20474 −5.49868 6.933432 1.20474 −6.98205 5.647655 1.20474 −8.62236 4.404171 1.20474 −10.4328 3.258442 1.20474 −12.4206 2.275387 1.20474 −14.5688 1.508892 1.20474 −16.8384 0.993132 1.20474 −19.1827 0.738138 1.20474 −21.5755 0.718305 1.20474 −23.9817 0.882545 1.20474 −26.3789 1.155668 1.20474 −28.7545 1.459452 1.20474 −31.1007 1.723931 1.20474 −33.422 1.892915 1.20474 −34.7245 1.928829 1.20474 −35.9544 1.918139 1.20474 −37.1105 1.862795 1.20474 −38.1934 1.763425 1.20474 −39.2036 1.618101 1.20474 −40.1413 1.423491 1.20474 −41.0063 1.177416 1.20474 −41.7986 0.879656 1.20474 −42.5182 0.52989 1.20474 −43.165 0.128125 1.20474 −43.739 −0.32564 1.20474 −44.2403 −0.83141 1.20474 −44.6689 −1.38919 1.20474 −45.0247 −1.99896 1.20474 −45.3078 −2.66074 1.20474 −45.5181 −3.37452 1.20474 −45.6556 −4.14029 1.20474 −45.7205 −4.95808 1.20474 −45.7125 −5.82786 1.20474

In the above Table 1, the plane Zadim=0 corresponds to the reference plane P0 situated at the base of the profile. This plane P0 is the intersection of the stacking axis AE of the set of vanes with the axisymmetric surface of the hub, i.e. it passes via the intersection between the axis AE and the surface where it is assembled with the inner shroud. The plane Zadim=1 corresponds to the reference plane P1 situated at the top of the profile. This plane P1 is the intersection between the axis AE and the axisymmetric surface of the casing, i.e. it passes via the intersection of the axis AE with the surface where it is assembled with the outer ring.

By convention, the stacking axis AE of a vane of a nozzle, is an axis that extends in the radial direction Z and is an axis on which the various X,Y sections of the set of vanes are “stacked” when designing the set of vanes.

As mentioned at the beginning of the present description, the aerodynamic profile of the disclosure is substantially identical to the nominal profile defined in the above table, i.e. it departs from said nominal profile by very little at most, being defined in particular within an envelope of ±1 mm in a direction normal to the surface of the nominal profile, and/or having X,Y coordinates lying within a range of ±5% relative to the coordinates X,Y of the nominal profile. Also, the aerodynamic profile is positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the stacking axis of the vane. In other words, the stagger angle may vary by ±10°, particularly by ±5°, more particularly by ±3°.

The coordinate Zadim is non-dimensional, i.e. for a point P, situated at a distance D from the plane P0 (where D is measured along the axis Z), the value of Zadim is D/H, where H represents the total height of the profile as measured between the planes P0 and P1. Naturally, in the Table 1 above, by multiplying the coordinate Zadim by the height H, it is possible to obtain the complete coordinates of the vane.

By way of example, the total height H is preferably about 56 mm±10%. By way of example, the plane P0 is situated at a distance of about 423 mm±10% from the axis A.

In the above table, the profile is characterized by seventeen section planes at constant Zadim coordinates, for which the coordinates X and Y are specified. These seventeen section planes include seventeen section planes located between Zadim=0 and Zadim=1, and thus arranged in the fluid stream, these section planes being distributed from P0 to P1. The seventeen section planes also include four section planes which are substantially outside the fluid stream (two section planes with Zadim<0, and two section planes with Zadim>1), these four section planes being provided for ensuring geometric continuity of the stacking, close to the head and the foot, respectively. In each section plane at constant coordinate Zadim, the section of the profile is given by a continuous and smooth curve, interconnecting all of the points (X,Y). In each section plane, the profile is interpolated so as to generate a uniform profile. Between the section planes, the profile is to be interpolated so as to generate a complete vane, as homogeneous as possible.

It is advantageous for the nozzle that includes the vane of the disclosure to have 105 to 125 vanes, more particularly 114 vanes, that present aerodynamic profiles as defined above. 

What is claimed is:
 1. An aerodynamic profile of a turbine vane, the aerodynamic profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is a quotient D/H, where D is a distance of a point under consideration from a reference X,Y plane situated at a base of the nominal profile, and H is a height of said nominal profile measured from said reference plane out to an end of the turbine vane, where D and H are taken radially relative to an axial direction of a turbine, while the coordinate X is measured in the axial direction of the turbine, wherein said aerodynamic profile is defined within an envelope of ±1 mm in a direction normal to a surface of the nominal profile.
 2. An aerodynamic profile of a turbine vane, the aerodynamic profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is a quotient D/H, where D is a distance of a point under consideration from a reference X,Y plane situated at a base of the nominal profile, and H is a height of said nominal profile measured from said reference plane out to an end of the turbine vane, where D and H are taken radially relative to an axial direction of a turbine, while the coordinate X is measured in the axial direction of the turbine, wherein the coordinates X,Y of said aerodynamic profile lie within a range of ±5% relative to the coordinates X,Y of the nominal profile.
 3. An aerodynamic profile of a turbine vane, the aerodynamic profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is a quotient D/H, where D is a distance of a point under consideration from a reference X,Y plane situated at a base of the nominal profile, and H is a height of said nominal profile measured from said reference plane out to an end of the turbine vane, where D and H are taken radially relative to an axial direction of a turbine, while the coordinate X is measured in the axial direction of the turbine.
 4. The aerodynamic profile as claimed in claim 3, wherein the aerodynamic profile is positioned within ±10° with respect to a radial axis of the turbine vane, along which the coordinate Zadim is measured.
 5. The aerodynamic profile as claimed in claim 3, wherein the aerodynamic profile is positioned within ±5° with respect to a radial axis of the turbine vane, along which the coordinate Zadim is measured.
 6. The aerodynamic profile as claimed in claim 3, wherein the aerodynamic profile is positioned within ±3° with respect to a radial axis of the turbine vane, along which the coordinate Zadim is measured.
 7. The aerodynamic profile as claimed in claim 3, wherein the turbine vane is a nozzle vane forming a part of a stator of a turbine.
 8. A turbine, including a plurality of turbine vanes presenting the aerodynamic profile as claimed in claim
 3. 9. The turbine as claimed in claim 8, including a nozzle that is stationary in rotation, having 105 to 125 turbine vanes that present the aerodynamic profile.
 10. The turbine as claimed in claim 8, including a nozzle that is stationary in rotation, having 114 turbine vanes that present the aerodynamic profile.
 11. A turbine nozzle forming a portion of a turbine stator, including a plurality of turbine vanes, wherein all the turbine vanes of the nozzle present the aerodynamic profile as claimed in claim
 3. 12. The turbine nozzle as claimed in claim 11, including 105 to 125 turbine vanes that present the aerodynamic profile.
 13. The turbine nozzle as claimed in claim 11, including 114 turbine vanes that present the aerodynamic profile. 